142 lines
69 KiB
Plaintext
142 lines
69 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 102,
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"metadata": {},
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"outputs": [],
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"source": [
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"%matplotlib widget"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 103,
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"metadata": {},
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"outputs": [],
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"source": [
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"from sympy import Symbol, sin, atan, exp, solve, diff, simplify,Eq\n",
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"from sympy.plotting import plot, plot3d\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"b = [Symbol(f'b_{i}', positive=True, real=True) for i in range(11)]\n",
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"Fz = Symbol('F_z', positive=True, real=True)\n",
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"x = Symbol('x', real=True)\n",
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"\n",
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"def pacejka96():\n",
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" C = b[0]\n",
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" D = (b[1] * Fz + b[2]) * Fz\n",
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" B=((b[3]*Fz**2+b[4]*Fz)*exp(-b[5]*Fz))/(C*D)\n",
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" E = b[6] * Fz**2 +b[7] * Fz + b[8]\n",
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" Sh=b[9]*Fz+b[10]\n",
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" \n",
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" X = x + Sh\n",
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" y = D * sin(C * atan(B * X - E * ( B * X - atan(B * X))))\n",
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" Y = y\n",
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" return Y"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Pacejka coefficients\n",
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"b_vals = [\n",
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" 1.65,\n",
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" -150,\n",
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" 1750,\n",
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" 0,\n",
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" 229,\n",
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" 0.0,\n",
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" 0,\n",
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" 0,\n",
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" 0,\n",
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" 0,\n",
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" 0\n",
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"]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 106,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "65cd3424eeba49718b715b433cabed68",
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"version_major": 2,
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"version_minor": 0
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},
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"image/png": 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",
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"\n",
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" <div style=\"display: inline-block;\">\n",
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" Figure\n",
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" </div>\n",
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' width=640.0/>\n",
|
|
" </div>\n",
|
|
" "
|
|
],
|
|
"text/plain": [
|
|
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"<sympy.plotting.backends.matplotlibbackend.matplotlib.MatplotlibBackend at 0x7effe9b83250>"
|
|
]
|
|
},
|
|
"execution_count": 106,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"%matplotlib widget\n",
|
|
"\n",
|
|
"slip_ratio = Symbol('slip_ratio')\n",
|
|
"slip_angle = Symbol('slip_angle')\n",
|
|
"\n",
|
|
"slip_ratio_formula = pacejka96().subs({sym: val for sym, val in zip(b, b_vals)})\n",
|
|
"\n",
|
|
"plot(abs((slip_ratio_formula / (Fz * 1000)).subs({Fz: 2})), (x, -100, 100))"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": ".venv",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.13.2"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|